How can I fix the black parts after I apply subsurf?
It might be because the vertices in the mesh are not made properly positioned that the blender is not able to properly calculate how to apply the modifier. So try these:


Recalculate the normals properly using: "Shift+N"
Go to edit mode and remove duplicate vertices by "Merge by distance
option" (make sure you set the proper distance in the dropdown menu). Also, make sure 
that there aren't overlapping faces